The Weekly Challenge - 350

Early Bird Club members ONLY

Task 1: Good Substrings

Submitted by: Mohammad Sajid Anwar

You are given a string.

Write a script to return the number of good substrings of length three in the given string.

A string is good if there are no repeated characters.

Example 1

Input: $str = "abcaefg"
Output: 5

Good substrings of length 3: abc, bca, cae, aef and efg

Example 2

Input: $str = "xyzzabc"
Output: 3

Good substrings of length 3: "xyz", "zab" and "abc"

Example 3

Input: $str = "aababc"
Output: 1

Good substrings of length 3: "abc"

Example 4

Input: $str = "qwerty"
Output: 4

Good substrings of length 3: "qwe", "wer", "ert" and "rty"

Example 5

Input: $str = "zzzaaa"
Output: 0

Task 2: Shuffle Pairs

Submitted by: E. Choroba

If two integers A <= B have the same digits but in different orders, we say that they belong to the same shuffle pair if and only if there is an integer k such that A = B * k. k is called the witness of the pair.

For example, 1359 and 9513 belong to the same shuffle pair, because 1359 * 7 = 9513.

Interestingly, some integers belong to several different shuffle pairs. For example, 123876 forms one shuffle pair with 371628, and another with 867132, as 123876 * 3 = 371628, and 123876 * 7 = 867132.

Write a function that for a given $from, $to, and $count returns the number of integers $i in the range $from <= $i <= $to that belong to at least $count different shuffle pairs.

PS: Inspired by a conversation between Mark Dominus and Simon Tatham at Mastodon.

Example 1

Input: $from = 1, $to = 1000, $count = 1
Output: 0

There are no shuffle pairs with elements less than 1000.

Example 2

Input: $from = 1500, $to = 2500, $count = 1
Output: 3

There are 3 integers between 1500 and 2500 that belong to shuffle pairs.

1782, the other element is 7128 (witness 4)
2178, the other element is 8712 (witness 4)
2475, the other element is 7425 (witness 3)

Example 3

Input: $from = 1_000_000, $to = 1_500_000, $count = 5
Output: 2

There are 2 integers in the given range that belong to 5 different shuffle pairs.

1428570 pairs with 2857140, 4285710, 5714280, 7142850, and 8571420
1429857 pairs with 2859714, 4289571, 5719428, 7149285, and 8579142

The witnesses are 2, 3, 4, 5, and 6 for both the integers.

Example 4

Input: $from = 13_427_000, $to = 14_100_000, $count = 2
Output: 11

6 integers in the given range belong to 3 different shuffle pairs, 5 integers belong to 2 different ones.

Example 5

Input: $from = 1030, $to = 1130, $count = 1
Output: 2

There are 2 integers between 1020 and 1120 that belong to at least one shuffle pair:
1035, the other element is 3105 (witness k = 3)
1089, the other element is 9801 (witness k = 9)

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Last date to submit the solution 23:59 (UK Time) Sunday 7^th December 2025.

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